Martin, this may be impractical performance-wise, but Haskell offers magic data structures for searching. Have a look at Martin Escardo's blog post [1] on infinite search in finite time. There is a package on Hackage [2] implementing it. The `shapes` you get are compact, non-empty subsets of types. If you have a shape shape :: Data.Searchable.Set a then Data.Searchable.search (const True) shape will return some element of your shape. As far as I know nobody has ever used this data structure for solid geometry. You'd need to combine it with some implementation of exact reals [*] to have geometry in a product of closed intervals. A downside is that general intersections don't exist, since the shapes must be non-empty. But since images of searchable sets are searchable, you could define complicated shapes by starting with a simple one and distort it with a function. If your type of space is discrete, then the search function might resort to brute force enumeration if the shape was defined that way. -- Olaf [1] http://math.andrej.com/2008/11/21/a-haskell-monad-for-infinite-search-in-fin... [2] http://hackage.haskell.org/package/infinite-search [*] As far as I am aware there is no appropriate package on Hackage, but Haskell implementations exist in several theses.